{"paper":{"title":"On roots of Wiener polynomials of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Danielle Wang","submitted_at":"2018-07-28T18:50:21Z","abstract_excerpt":"The \\emph{Wiener polynomial} of a connected graph $G$ is the polynomial $W(G;x) = \\sum_{i=1}^{D(G)} d_i(G)x^i$ where $D(G)$ is the diameter of $G$, and $d_i(G)$ is the number of pairs of vertices at distance $i$ from each other. We examine the roots of Wiener polynomials of trees. We prove that the collection of real Wiener roots of trees is dense in $(-\\infty, 0]$, and the collection of complex Wiener roots of trees is dense in $\\mathbb C$. We also prove that the maximum modulus among all Wiener roots of trees of order $n \\ge 31$ is between $2n-15$ and $2n-16$, and we determine the unique tre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10967","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}